We study the cosmological constant ($\mathrm{\Lambda }$) in the standard $\mathrm{\Lambda }$ cold dark matter model by introducing the graduated dark energy (gDE) characterized by a minimal dynamical deviation from the null inertial mass density of the $\mathrm{\Lambda }$ in the form ${\rho }_{\text{inert}}\propto {\rho }^{\lambda }<0$ with $\lambda <1$ being a ratio of two odd integers, for which its energy density $\rho$ dynamically takes negative values in the finite past. For large negative values of $\lambda$, it creates a phenomenological model described by a smooth function that approximately describes the $\mathrm{\Lambda }$ spontaneously switching sign in the late Universe to become positive today. We confront the model with the latest combined observational datasets of $\mathrm{Planck}+\mathrm{baryon}\mathrm{acoustic}\mathrm{oscillations}+\mathrm{supernova}+H$. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative $\lambda$ values; the new maximum significantly excludes the $\mathrm{\Lambda }$, and the old maximum contains the $\mathrm{\Lambda }$. The improvement in the goodness of fit for the $\mathrm{\Lambda }$ reaches highly significant levels, $\mathrm{\Delta }{\chi }_{\min }^2=6.4$, for the new maxima, while it remains at insignificant levels, $\mathrm{\Delta }{\chi }_{\min }^2\lesssim 0.02$, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the $\mathrm{\Lambda }$, the new maxima agree with the model-independent $H_0$ measurements, high-precision $\mathrm{Ly}\text{−}\alpha$ data, and model-independent $Om{h}^2$ diagnostic estimates. Our results provide strong hints of a spontaneous sign switch in the cosmological constant and lead us to conjecture that the Universe has transitioned from anti-de Sitter vacua to de Sitter vacua, at a redshift $z\approx 2.32$, and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\mathsf{\Lambda }$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

We explore an extension of the ΛCDM model in which the pressure p of the dark energy (DE) fluid evolves with the expansion of the Universe, expressed as a function of the scale factor a. The corresponding energy density ρ is derived from the continuity equation, resulting in a dynamical equation-of-state parameter w ≡ p/ρ during the late-time expansion of the Universe. The pressure is modeled using a Taylor expansion around the present epoch (a = 1), introducing deviations from a cosmological constant within the dynamical dark energy (DDE) framework. At first order, a single new parameter Ω₁ captures linear deviations, while a second-order parameter, Ω₂, accounts for quadratic evolution in the pressure. We constrain the first- and second-order DDE models using multiple observational datasets and compare their performance against ΛCDM and the CPL parameterization. A joint analysis of Planck CMB, DESI, and DESY5 data yields the strongest evidence for DDE, with a 2.7σ deviation in the first-order model and over 4σ in the second-order model — providing strong statistical support for a departure from a cosmological constant. The reconstructed DE evolution in the second-order case reveals a distinctive non-monotonic behavior in both energy density and w _DE(a), including clear phantom-crossing phenomena. Notably, the late-time evolution of w _DE(a) remains consistent across datasets and shows strong agreement with the CPL parameterization, underscoring the robustness of the pressure-based approach.

The main aim of this paper is to perform a model comparison for some reconstructions of the key properties that describe the dark energy of the Universe i.e. energy density and the equation of state (EoS). We carry out this process by using a binning and a linear interpolation methodologies, and on top of that, we incorporate a correlation function mechanism. An extension of the two of them was also introduced, where internal amplitudes are allowed to vary in height as well as in position. The reconstructions were made with data from the Hubble parameter, Supernovae Type Ia and Baryon Acoustic Oscillations (H+SN+BAO), all of which span a range from $$z=0.01$$z = 0.01 to $$z=2.34$$z = 2.34 . First we perform the parameter estimation for each of the reconstructions to then provide a model selection through the Bayesian Evidence. Throughout our process we found a better fit to the data, up to $$4\sigma $$4 σ compared to $$\Lambda $$Λ CDM, and the presence of some interesting features, i.e. an oscillatory behaviour at late times, a decrease in the dark energy density component at early times and a transition to the phantom divide-line in the EoS. To discern these features from noisy contributions, we include a principal component analysis and found that some of these characteristics should be taken into account to satisfy current observations.

Baryon acoustic oscillation (BAO) measurements play a key role in ruling out postrecombination solutions to the Hubble tension. However, because the data compression leading to these measurements assumes a fiducial Λ CDM cosmology, their reliability in testing late-time modifications to Λ CDM has at times been called into question. We play devil’s advocate and posit that fiducial cosmology assumptions do indeed affect BAO measurements in such a way that low-redshift acoustic angular scales (proportional to the Hubble constant H 0 ) are biased low and test whether such a rescaling can rescue postrecombination solutions. The answer is no. First, strong constraints on the shape of the z ≲ 2 expansion history from unanchored Type Ia Supernovae (SNeIa) prevent large deviations from Λ CDM . In addition, unless Ω m is significantly lower than 0.3, the rescaled BAO measurements would be in strong tension with geometrical information from the cosmic microwave background. We demonstrate this explicitly on several dark energy (DE) models ( w CDM , CPL DE, phenomenologically emergent DE, holographic DE, Λ s CDM , and the negative cosmological constant model), finding that none can address the Hubble tension once unanchored SNeIa are included. We argue that the Λ s CDM sign-switching cosmological constant model possesses interesting features which make it the least unpromising one among those tested. Our results demonstrate that possible fiducial cosmology-induced BAO biases cannot be invoked as loopholes to the Hubble tension “no-go theorem”, and highlight the extremely important but so far underappreciated role of unanchored SNeIa in ruling out postrecombination solutions.